𝐿^{𝑝} approximation of Fourier transforms and certain interpolating splines

Shreve, David C.

doi:10.1090/S0025-5718-1974-0383803-4

$L^{p}$ approximation of Fourier transforms and certain interpolating splines
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by David C. Shreve PDF

Math. Comp. 28 (1974), 779-787 Request permission

Abstract:

We extend to ${L^p},1 \leqq p \leqq \infty$, the ${L^2}$ results of Bramble and Hilbert on convergence of discrete Fourier transforms and on approximation using smooth splines. The main tools are the estimates of [1] for linear functionals on Sobolev spaces and elementary results on Fourier multipliers.

References

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